Well there's the Timothy Eaton statue on the 2nd floor of the arena - rub his toe for good luck...and a bit of stuff inside the arena on the 100-level concourse.
Food nearby - across Portage Avenue from the MTSC is the Merchant Kitchen in the Alt Hotel - Latin/Asian, and it's quite good. Moxie's in the MTSC is okay...it's a chain with some aspirations, so the food's half decent.
Food elsewhere in town - what are you after? 529 Wellington is the high-end steakhouse. VJ's on Main is a good place for fatboys/burgers/fries. Resto Gare on Des Meurons in St. Boniface for French/Canadian/Manitoban fare. Fergies Fish and Chips is at the Forks. Stella's on Sherbrook (or Grant, or Osborne? there are a few around) for brunch. Pizzeria Gusto on Academy. Kum Koon Garden on King for Dim Sum. I'm ashamed to admit I don't know where to get good Ukrainian food now that Alycia's moved out of town...
Cultural stuff - the Art Gallery is about 8 blocks west of the MTSC. The Exchange District starts 2 or 3 blocks northeast of MTSC. Dress for winter if you're going to stroll around there. The Zoo's Journey to Churchill exhibit is pretty cool (NO PUN INTENDED
) but it's not near downtown.